# Article

Ufa Mathematical Journal
Volume 3, Number 4, pp. 42-55

# On decay rate of solution for degenerating linear parabolic equation

Gilimshina V.F., Mukminov F.Kh.

Existence and uniqueness of solution to linear degenerating parabolic equation is established on unbounded domains by the method of Galerkin's approximations. The first and the therd boundary conditions are considered. Upper estimate of decay rate of solution as $x\to\infty$ is established . Upper estimate of decay rate of solution $t\to\infty$ depending on geometry of unbounded domain is proved.